Method and System for Rendering 3D Distance Fields

Abstract

A method and system renders a 3D model of a 3D object as an image including image samples. The 3D model is a distance field, and the distance field includes surface cells representing portions of a surface of the 3D object. A set of image samples in the image is determined in an object-order phase for each surface cell. Each surface cell is then processed independent of other surface cells. The processing casts a ray, in an image order phase from each image sample in the set of image samples, through the surface cell to determine a contribution of the surface cell to the image sample, and then the image is rendered.

Description

FIELD OF THE INVENTION[0001]This invention relates generally to the field of computer graphics and to rendering 3D models of 3D objects, and more particularly to rendering the 3D models of the 3D objects where the 3D models are represented as 3D distance fields, and used to simulate the results of computer numerically controlled (CNC) machining operations.BACKGROUND OF THE INVENTION[0002]Distance Fields[0003]In computer graphics applications, a three-dimensional (3D) object can be represented using a number of different methods, e.g., methods that use polygonal models, point cloud models, parametric functions, or implicit functions.[0004]One class of methods uses a distance field that specifies a minimum distance d(x) from any location x=(x, y, z) in 3D space to a surface of the object. The distance field d(x) can distinguish the inside, the outside and the surface of the object, e.g., d(x)<0 is outside, d(x)>0 is inside, and d(x)=0 is on the surface of the object.[0005]Furthe...

AI Technical Summary

Benefits of technology

[0030]It is desired to provide a method for rendering the surface represented by the 3D distance field that has the accuracy of ray casting, and the speed of polygon rendering. Additionally, it is desired that this method for rendering produces images without any crack artifacts.

[0031]It is also desired to provide a simulation that can be incorporated into manufacturing operations such as performed by milling and other machine tools. Such a simulation would enable the operator to visually identify mistakes in the machining process before the part is actually machined, thereby saving time and possibly materials.SUMMARY OF THE INVENTION

Problems solved by technology

However, it can be difficult to create images without holes.

Uniform coverage of the surface with points is not guaranteed and considerable effort is required to identify and fill in missing regions.

The process of identifying surface cells in the octree that contain the surface along the direction of the cast ray is fairly simple, but can be very inefficient in terms of computer memory accesses.

The data associated with spatially adjacent cells in the octree are often widely separated in computer memory, resulting in a high rate of CPU memory cache misses, which degrades the overall performance of the rendering method.

When the data required for casting rays through a cell are not in the CPU cache as needed, the rendering update rate is severely decreased, sometimes to the point that interactive rendering while manipulating the model at real-time rates, e.g., ten updates per second, is impossible.

This results in images that are more faceted in appearance, and therefore cannot accurately represent curved surfaces.

This is a particular problem when the rendering must be highly accurate, e.g., accurate to one part in a 106.

With polygon rendering, it may be necessary to employ an unmanageably large number of very small polygons to produce surface images that are very smooth resulting in extreme memory and / or processing requirements.

As a result, the surface reconstructed from the distance field samples of one cell may not exactly match the surface reconstructed from the distance field samples of an adjacent cell resulting in the appearance of cracks in the rendered image.

Images